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# Logarithmic Functions

Logarithmic scales are used when the range of possible values is very wide, such as the intensity of an earthquake or the acidity of a liquid, in order to avoid the use of large numbers.

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Evaluate the following:

\[ \Large 9^{\log_{3}(4)} \]

Do not use a calculator -- not even a slide rule!

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Dmytri Eck**

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\[ \large \log_2 3 \times \log_3 4 \times \log_4 5 \times \cdots\times \log_{127} 128 = \, ? \]

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حسن العطية**

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**True or false**:

\(\quad \quad \) \(\log_{x}1=0\) for every \(x>0\).

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Hjalmar Orellana Soto**

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\[ \large \sum_{\text{cyclic}(a,b,c)} \left( \dfrac1{1 + \log_a bc} \right) = \, ? \]

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Abhiram Rao**

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Which of the options is correct about the number \(\log _{ 4 }{ 18 } \)?

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Anandhu Raj**

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